According to 1938 Romanian Encyclopaedia, "The 1866 Constitution as well as
the Law for establishing the coat of arms of Romania from 1867 (art. 6) and the
Law for changing the country's coat of arms from 1872 (art. 6) stated the
[vertical] arrangements of the [flag] colours... Same laws established that the
army flag will bear in the middle the country's coat of arms and the civil flag
will not bear any coat of arms". So, according to the law, the military flag
should bear the entire Romanian coat of arms in the middle, on the yellow strip.
However, by use, the coat of arms was surrounded by two olive branches and in
every corner there was the king's monogram surrounded itself by 2 olive
branches.Alex Danes, 8 January 2008

The Romanian Constitution from 1866 (30 June) stated at article 124 that the colors of the country will be blue, yellow and red. It didn't establish an orientation, order, or coat of arms.
The Romanian laws regarding the state coat of arms and flags from 1867 (24 April) and 1872 (23 March) are quite similar, the only difference being the coat of arms described. Articles 1 to 5 deals with the coat of arms, and articles 6 to 9 with flags. Since the last ones are identical, i'll present them first:

Art. 6. The princely flag and the Army's flag will have the colors placed like this:
Blue perpendicular (sic!), near the hoist, yellow in the middle and red floating. In the middle there will be the country's coat of arms.Art. 7. The flag of Civic guard will be identical to the Army's one, replacing the coat of arms of the country with the coat of arms of the city and the number of the legion.Art. 8. The civil flag will be identical to the Army's one, without the coat of arms in the middle.Art. 9. The war ensign will be identical to the Army's one, with the coat of arms in the middle.
The merchant ensign will be identical to the war ensign, without the coat of arms in the middle.

Quarterly: I Azure an eagle Sable with its head to sinister, a cross Sable in its beak, a sun Or on its sinister; II Azure an aurochs' head Sable, a six-pointed star Argent between its horns, a crescent Argent on its dexter; III Gules an aurochs' head Sable, a six-pointed star Argent between its horns; IV Or an eagle Sable with its head to the sinister, a cross Sable in its beak. Overall, the shield of Hohenzollern house: quarterly Argent and Sable.
The shield is crowned with a royal crown Or and it is supported by a Dacian women at dexter in natural colors, with a sword in her right hand, and a leopard-lionee Or at senester. Both are standing on a scroll Azure lined with Gules, with the motto "Nihil sine Deo" Or (Nothing without God).
The coat of arms is placed on a mantle Gules lined with Ermine. Above the mantle is a royal crown Or.Alex Danes, 29 August 2008

Quarterly: I Azure an eagle Or with its head to sinister, a cross Or in its beak, a sword Or in dexter claw, a mace Or in senester claw, a sun Or on its dexter; II Gules an aurochs' head Or, a six-pointed star Or between its horns, a crescent Or on its senester; III Gules a rampant lion Or, with a coronet Or, holding a six-pointed star Or between its paws, standing on a coronet Or; IV Azure two dolphins Or, affronts, head down. Overall, the shield of Hohenzollern house: quarterly Argent and Sable.
The shield is crowned with a royal crown Or and it is supported by two rampant lions Or, with their tails between their legs. Both are standing on a scroll Azure lined with Gules, with the motto "Nihil sine Deo" Or (Nothing without God).
The coat of arms is placed on a mantle Gules lined with Ermine. Above the mantle is a royal crown Or.Alex Danes, 29 August 2008

In 1877-1878 Romania gained its independence from the Ottoman Empire. In 1881 prince Charles I was crowned king. This events also reflected on the coat of arms. The supporters had their tails moved behind their back, the royal crown above the mantle was replaced with the Romanian Steel Crown and the National Order "Star of Romania" appeared beneath the scroll Azure. This changes were not reflected by the law; nevertheless, the slightly modified model replaced the 1872 one almost everywhere, including official papers, prints and flags.Alex Danes, 29 August 2008

Briefly, on March 30th, 1867 the first Romanian law on the Royal Standard stated that it had to
match the war ensign. Consequently, the king used the war ensign and his
standard followed the evolution of that ensign till the kingdom of Charles I.Pier Paolo Lugli, 7 January 2003

According to the existing law, the royal standard should have been identical to the Army flag, that is the Romanian blue-yellow- red tricolor, proportion 2:3, with the coat of arms in the middle of the yellow stripe. The 1867 official model had the coat of arms established on 24 April 1867.Alex Danes, 27 August 2008

by Alex Danes

On 23 March 1872 the coat of arms was changed, and thus the flags themselvs.Alex Danes, 27 August 2008

1:1, by Alex Danes

Somewhere after 1872, the standard was slightly changed by use, and not by law.Alex Danes, 27 August 2008

Square flag with yellow field, a blue border at hoist and red and fly, in the
middle the coat of arms and in each corner a royal crown. The coat of arms is of
the 1881 pattern (when Romania became a kingdom), and differs only marginally
from the 1872 pattern (by addition of the Order of the Crown of Romania). The
crowns in the corners appear black and white in the
National Geographic (1917) image, but I concluded that this is due to the
printing (in)abilities and I have used the fully-coloured crown (actually the
one from Calvin's 1939 Reserve Ensign). If anyone has access to an independent
source of this flag maybe they can confirm this choice of mine.Željko Heimer, 28 December 2002

About 1900 king Charles determined to change his standard blue-yellow-red
proportions into 1:4:1, adding to each canton an upright steel crown. The arms
remained at the center of the yellow stripe.Pier Paolo Lugli, 7 January 2003

According to the Enciclopedia of Romania, "When the princely and later royal standard was made, the yellow stripe was twice wider than the red and blue one. In the middle of the yellow stripe had been sewn the Romanian coat of arms, and in each of the corners of the flag a royal silver crown.". This means that the standard had a 1:2:1 proportion, that it was used even before Charles I of Romania was crowned king (1881), and that the royal crowns in the corners are silver, not golden, as mr. Željko Heimer supposed.Alex Danes, 27 August 2008